Question: Christopher is 2 times as old as Omar. Twenty years ago, Christopher was 6 times as old as Omar. How old is Omar now?
Answer: We can use the given information to write down two equations that describe the ages of Christopher and Omar. Let Christopher's current age be $c$ and Omar's current age be $o$ The information in the first sentence can be expressed in the following equation: $c = 2o$ Twenty years ago, Christopher was $c - 20$ years old, and Omar was $o - 20$ years old. The information in the second sentence can be expressed in the following equation: $c - 20 = 6(o - 20)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $o$ , it might be easiest to use our first equation for $c$ and substitute it into our second equation. Our first equation is: $c = 2o$ . Substituting this into our second equation, we get: $2o$ $-$ $20 = 6(o - 20)$ which combines the information about $o$ from both of our original equations. Simplifying the right side of this equation, we get: $2 o - 20 = 6 o - 120$ Solving for $o$ , we get: $4 o = 100.$ $o = 25$.